高维哈达码矩阵理论与应用
2006-7
科学
Yixian Yang
无
111111
preface.
part i two-dimensional cases
chapter 1 walsh matrices
1.1 walsh functions and matrices
1.1.1 definitions
1.1.2 ordering
1.2 orthogonality and completeness
1.2.1 orthogonality
1.2.2 completeness
1.3 walsh transforms and fast algorithms
1.3.1 walsh ordered walsh-hadamard transforms
1.3.2 hadamard ordered walsh-hadamard transforms
bibliography
chapter 2 hadamard matrices
2.1 definitions
2.1.1 hadamard matrices
2.1.2 hadamard designs
2.1.3 williamson matrices
2.2 construction
2.2.1 general constructions
.2.2.2 amicable hadamard matrices
2.2.3 skew hadamard matrices
2.2.4 symmetric hadamard matrices
2.3 existence
2.3.1 orthogonal designs and hadamard matrices
2.3.2 existence results
bibliography
part ii lower-dimensional cases
chapter 3 three-dimensional hadamard matrices
3.1 definitions and constructions
3.1.1 definitions
3.1.2 constructions based on direct multiplications
3.1.3 constructions based on 2-dimensional hadamard matrices
3.2 three-dimensional hadamard matrices of order 4k + 2
3.3 three-dimensional hadamard matrices of order 4k
3.3.1 recursive constructions of perfect binary arrays
3.3.2 quasi-perfect binary arrays
3.3.3 3-dimensional hadamard matrices based on pba(2m, 2m) and pba(3.2m, 3.2m)
3.4 three-dimensional walsh matrices
3.4.1 generalized 2-dimensional walsh matrices
3.4.2 3-dimensional walsh matrices
3.4.3 3-dimensional pan-walsh matrices
3.4.4 analytic representations
bibliography..
chapter 4 multi-dimensional walsh-hadamard transforms
4.1 conventional 2-dimensional walsh-hadamard transforms
4.1.1 2-dimensional walsh-hadamard transforms
4.1.2 definitions of 4-dimensional hadamard matrices
4.2 algebralcal theory of higher-dimensional matrices
4.3 multi-dimensional walsh-hadamard transforms
4.3.1 transforms based on 3-dimensional hadamard matrices
4.3.2 transforms based on 4-dimensional hadamard matrices
4.3.3 transforms based on 6-dimensional hadamard matrices
bibliography
part iii general higher-dimensional cases
chapter 5 n-dimensional hadamard matrices of order 2
5.1 constructions of 2n hadamard matrices
5.1.1 equivalence between 2n hadamard matrices and h-boolean functions
5.1.2 existence of h-boolean functions
5.1.3 constructions of h-boolean functions
5.2 enumeration of 2n hadamard matrices
5.2.1 classification of 24 hadamard matrices
5.2.2 enumeration of 25 hadamard matrices
5.2.3 enumeration of general 2n hadamard matrices
5.3 applications
5.3.1 strict avalanche criterion and h-boolean functions
5.3.2 bent functions and h-boolean functions
5.3.3 reed-muller codes and h-boolean functions
bibliography
chapter 6 general higher-dimensional hadamard matrices
6.1 definitions, existences and constructions
6.1.1 n-dimensional hadamard matrices of order 2k
6.1.2 proper and improper n-dimensional hadamard matrices
6.1.3 generalized higher-dimensional hadamard matrices
6.2 higher-dimensional hadamard matrices based on perfect binary arrays
6.2.1 n-dimensional hadamard matrices based on pbas
6.2.2 construction and existence of higher-dimensional pbas
6.2.3 generalized perfect arrays
6.3 higher-dimensional hadamard matrices based on orthogonal designs
6.3.1 definitions of orthogonality
6.3.2 higher-dimensional orthogonal designs
6.3.3 higher-dimensional hadamard matrices from orthogonal designs
bibliography
concluding questions
index...
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